June 2, 2003
Problem of the Week

Magic Square

The following is an example of a magic square, five of whose entries are missing. Determine the missing entries A, B, C, D, and E so the sum of each row, column, and diagonal is the same.

A	B	10.5
6.75	C	D
8	E	5.5

Solution to the Problem:

The answer is:

A = 13
B = 4.25
C = 9.25
D = 11.75
E = 14.25

13	4.25	10.5
6.75	9.25	11.75
8	14.25	5.5

Since the 3 numbers in each row must be the same, equate the middle row and the last column to find C:
6.75 + C + D = 10.5 + D + 5.5
Therefore C = 16 - 6.75 = 9.25

Then the magic sum must be 8 + 9.25 + 10.5 = 27.75.
Therefore, A = 13
B = 4.25
E = 14.25 and
D = 11.75

Correctly solved by:

1. Rick Jones	Kennett Square, Pennsylvania
2. Walt Arrison	Philadelphia, Pennsylvania
3. Richard Johnson	La Jolla, California
4. William Funk	San Antonio, Texas
5. Misty Carlisle	Winchester, Virginia
6. John Funk	Ventura, California
7. John Beasley	Winchester, Virginia
8. James Alarie	University of Michigan -- Flint, Flint, Michigan
9. Bob Hearn	Winchester, Virginia
10. Dash Waughquasebarth	Winchester, Virginia
11. Jeffrey Gaither	Winchester, Virginia
12. George Gaither	Winchester, Virginia
13. Josh Feingold	Winchester, Virginia
14. Kirstine Wynn	Bellingham, Washington
15. David and Judy Dixon	Bennettsville, South Carolina

Send any comments or questions to: David Pleacher